1. Field of the Invention
The present invention relates to a transducer device for an acoustic log, including a transmitter sending a signal within a lobe region and at least two receivers, provided for receiving signals reflected from a reference for determining the velocity component of a vessel relative to the reference in the measuring direction determined by the two receivers.
2. Background of the Discussion
Such devices in which the velocity determination takes place with the use of correlation technique are already known from U.S. Pat. Nos. 3,991,398, 4,041,293 and 4,068,207. Two similar, but mutually time-shifted signals are then generated, the time-shift of which depends on the distance in the measuring direction between the two receivers and on the velocity of the vessel.
The principle for velocity measurement using a correlation technique, which is carried out by the transducer device in accordance with the invention, is described in the above-mentioned patents. A short description of the principle is given below, and for the sake of simplicity, the signals are assumed to be continuous.
Two signals S.sub.1 (t) and S.sub.2 (t) mutually time-shifted by time t.sub.0 (see FIG. 1), and a sample system where the sample is taken with the interval t.sub.s are used.
The following product is calculated for each new sample. ##EQU1##
The development of this product gives: ##EQU2## where AKF denotes the autocorrelation function, and KKF denotes the cross correlation function.
These functions are illustrated in FIG. 2. The functions AKF and KKF intersect at the point t.sub.s =t.sub.0 /2. Another interesting property is that S.sub.11 -S.sub.23 =0 for t.sub.s =t.sub.0 /2, which signifies that the estimate of E has little variance about the intersection point.
A velocity measuring system is provided by the sampling interval t.sub.s being controlled such that AKF=KKF, which results in the velocity v being obtained as EQU v=1.sub.0 /2t.sub.s
where 1.sub.0 denotes the measuring base, i.e. the distance between the crystals used, as will be described in greater detail below.
In the evaluation of the time delay t.sub.0 between the receiver signals the difference between the autocorrelation function and the cross correlation function, AKF-KKF, is thus used. This function is illustrated in FIG. 3 and its zero passage thus gives t.sub.0 /2.